Generalized Kazdan-Warner equations associated with a linear action of a torus on a complex vector space
Differential Geometry
2023-05-30 v4
Abstract
We introduce generalized Kazdan-Warner equations on Riemannian manifolds associated with a linear action of a torus on a complex vector space. We show the existence and the uniqueness of the solution of the equation on any compact Riemannian manifold. As an application, we give a new proof of a theorem of Baraglia which asserts that a cyclic Higgs bundle gives a solution of the periodic Toda equation.
Cite
@article{arxiv.2002.09141,
title = {Generalized Kazdan-Warner equations associated with a linear action of a torus on a complex vector space},
author = {Natsuo Miyatake},
journal= {arXiv preprint arXiv:2002.09141},
year = {2023}
}
Comments
The numbering of theorems, propositions, examples, corollaries, lemmas, definitions, and remarks has been made the same as in the published version. 23 pages